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Appendix V.




P. 363. Connection of the Moduli E, C, and K. 

Consider a cube A Y B x, Fig. 916, under the action of pure shear
stress and strain, and let Y move to y under shear. Then x Y
extends to xjy under^tension (see pp. 366 and 755). But XY, the
original length  Jz, and x z = ^2, and vy is 8S.

zy =  -L



Total extension

total extension            &s

-  -  --- -.     =    j^-2  7=

original length        ^2  ^2

In like manner 8C = ^ s, and a pure shear strain in one
direction consists of two direct strains, compressive and tensile, each
having a value half the shear strain,

or    5C s= 5t   s

But it has already been proved at pp.' 366 and 755 that two
stresses, compressive and tensile, of equal intensity, cause a third
stress in shear of the same intensity,

or   /c == /t = /s

Still considering the inch cube,

LetM = ^ (Poisson's ratio)        and let ~ =* a
j3                                             E